3 Answers
3

I think the best way to look at this would be to consider what one is trying to convey.

This could also read "knowledge my class had concerning the real Pocahontas." The word concerning often takes the genitive case in Greek and Latin, which relates to the word of. However, the expression "on the real Pocahontas" would take the ablative case in Latin and would not coincide with concerning. Therefore, the sentence

She tried to figure out how much knowledge my class had of the
real Pocahontas.

The preposition of is generally used with knowledge: "knowledge of (something)".

her considerable knowledge of antiques
he denied all knowledge of the incidents

However, it is important to note here that the question relates not to some personal acquaintance with Pocahontas ("knowledge of Pocahontas"), but an understanding of the concept ("knowledge on Pocahontas").

If the pupils have studied and understood the story, they would have such an understanding.

Without a credible data sharing mechanism, building strategic knowledge on climate change is virtually impossible.
General Knowledge on the Use of Medicines

We need to use the preposition on in the example sentence.

She tried to figure out how much knowledge my class had on the real Pocahontas.

It could also be that "knowledge of" goes with a person or shows one's familiarity with someone or something (cf. the verb kennen in German) and "knowledge on" or "knowledge about" (cf. the verb wissen in German) goes with a field of study or a broad subject where one's personal attachment to it is irrelevant.

It also seems that "knowledge about" could be used in either case; it's just a longer form that may not be desired if someone's trying to write poetic verse or a terse newspaper headline, for example.